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It's a paradox: mathematics, the pure science par excellence, does not rest on mathematizable foundations. This was demonstrated by Kurt Gödel. An implacable logician, the Austrian was also in poor mental health. A severe hypochondriac, he believed in spirits, demons, ghosts and life after death, but he remains THE mathematician who most revolutionized the logical foundations of mathematics in the 20th century. And one of the first to attempt to demonstrate mathematically the existence of God...
Kurt's childhood was fertile ground for his passion for questions and puzzles. From an early age, he amazed those around him with his insatiable curiosity, asking incessant questions about everything around him. His relentless quest for answers earned him the nickname "Der Herr Warum" (Mr. Why). A brilliant student, he distinguished himself particularly in mathematics, obtaining only one mark below the maximum throughout his primary and secondary schooling.
Although Gödel initially excelled in languages, speaking and writing perfect French and English, he soon realized that physics, the discipline in which he began his studies alongside his brother at the University of Vienna, lacked precision. So he turned to mathematics and logic, fields that offered the rigor and clarity he was looking for.
At the age of 25, Gödel published his most important results, including the Incompleteness Theorem for which he became famous. This theorem, the cornerstone of his work, asserts that any logical system powerful enough to describe the arithmetic of integers contains undecidable propositions, i.e. statements that can be neither invalidated nor confirmed on the basis of the theory's axioms. His demonstration became a classic of mathematical reasoning and propelled Gödel to international fame in the world of mathematics.
The First Incompleteness Theorem was only the beginning of a series of achievements for Gödel. Although his 1931 paper only sketched the outline of the Second Incompleteness Theorem, his proof was so well accepted by the mathematical community that he saw no need to specify it further. With this feat, Gödel put an end to Hilbert's hopes of completely axiomatizing mathematics, thus proving that mechanical deduction cannot be the sole foundation of this science, leaving room for intuition. Unfortunately, neither Zermelo, Russell nor Wittgenstein fully grasped the meaning and significance of these theorems, giving rise to numerous misinterpretations that persist to this day.
Gödel and Einstein first met in the United States, where both geniuses had fled from Europe to escape the rise of the Nazi regime. They shared a common passion for scientific research, but it was their intellectual affinity and mutual understanding that sealed their exceptional friendship.
Beyond their respective fields, Gödel and Einstein inspired and stimulated each other intellectually. Their friendship was based on a mutual admiration and fascination for the fundamental questions of the universe. They engaged in passionate discussions, exploring topics ranging from the philosophy of knowledge to the nature of time and space.
The friendship between Gödel and Einstein was nourished not only by deep intellectual conversations, but also by close personal ties. The two men shared common values and a similar worldview. Their shared exile and experience of Nazi persecution brought them even closer together, strengthening their mutual support and friendship.
A fascinating anecdote from this friendship relates to Gödel's application for American citizenship. Obsessed with logic and accuracy, he dared to demonstrate, during his interview, the contradictions present in certain articles of the US Constitution. This bold, if surprising, gesture reflected his relentless quest for truth and logical integrity, even when confronted with official situations.
At Princeton, Gödel distinguished himself by his unusual behavior and peculiar ideas. Convinced that his refrigerator and radiators emitted toxic substances, he had them replaced on numerous occasions and frequently moved from one apartment to another. His perception of history and current affairs often baffled those around him.
Gödel's juxtaposition of valuable scientific ideas, questionable philosophical and religious opinions, superstitious beliefs and pathological disorders can be disconcerting. However, all these elements were intrinsically linked to his personality. Convinced that nothing happens by accident, Gödel expressed extreme rationalism mixed with paranoia, feeding his attraction to the supernatural and the occult.
Although mentally ill, Kurt Gödel managed to become a naturalized citizen thanks to the support of his friends Oskar Morgenstern and Albert Einstein. After the war, he entered Princeton University on a permanent basis, but in the mid-1970s, his troubles turned into persecutory delusions, hastening his demise. Interned at Princeton Hospital, he succumbed on January 14, 1978, weighing just 29.5 kg.
Despite his death, Gödel's legacy remains immense. In addition to his publications, he left behind numerous unpublished manuscripts, mainly on philosophy and theology. His ontological proof of the existence of God, inspired by the work of Anselm of Canterbury and Leibniz, circulated among his friends. On the eve of his 70th birthday, the deeply mystical Gödel attempted to demonstrate the existence of God, combining logic and faith in a profound reflection on metaphysical questions.
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